A connotation is a word that has two meanings: its literal interpretation and the cultural interpretation that it is given. Many phrases that we use today in our language have no literal meaning in the context in which we use them, however they have come to be accepted as having a secondary meaning, such as "raining cats and dogs."
In "A & P," we are given a first-person account from a young man, who, understandably, expresses things as he sees them one day working behind the till from his own cultural understanding. Thus it is that this account contains many connotations. Consider the following examples:
By the time I got her feathers smoothed and her goodies into a bag... the girls had circled round the bread and were coming back.
Note how the expression "feathers smoothed" refers to the "witch" of a customer that the narrator was serving as the girls entered. This literally of course has no meaning: the woman has no feathers, but the narrator is referring to calming her down and restoring her composure after she has just "given him hell." This of course is another connotation. The woman is unable to literally give "him hell," but it refers to her sudden anger and annoyance when the narrator accidentally rings one of her purchases up twice.
So, hopefully with these two examples you will be able to go on and re-read this excellent story, looking for more examples of connotation. Good luck!